Statistics Probability

In a pencil box, 7 out of 20 pencils have an eraser and 8 out of 20 are mechanical. There are 4 pencils that are both mechanical and have an eraser on them. What is the probability of choosing a pencil at random and getting either a mechanical pencil or a pencil with an eraser? Please explain.

1. Why are we adding the pencils that are mechanical with an eraser? It says Mechanical pencil or a pencil with an eraser.

2. 7 out of 20 pencils have an eraser. 8 out of 20 are mechnical. 4 pencils are both mechanical and have an eraser. 7 pencils with an eraser + 8 mechanical pencils = 15, what about the other 5 pencils...what are they? There's 20 pencils in the box, we only have information on 15 of them. Are they pencils without an eraser and aren't mechanical?

the pencils that are mechanical with erasers count as either mechanical pencils or pencils with erasers, so the 4 pencils that are mechanical with eraser have been counted twice, so we only have information on 7+8 -4 =11 pencils, the other 9 pencils are not mechanical, neither they have erasers.